Explanation Given: The functions are y = 2 x , y = 0 , x = 8 , and axis x = − 3 . Formula used: Volume V = ∫ a b A ( x ) d x Where a ≤ x ≤ b and A = 2 π r h . Calculation: The functions are y = 2 x , y = 0 , x = 8 , and axis x = − 3 . The graphs of y = 2 x and y = 0 intersect where 2 x = 0 x = 0 The graph of the function is: Thus, the enclosed area lies over the interval [ 0 , 8 ] . Choose the slice of region bounded by the graphs y = 2 x , y = 0 , and x = 8 verticallyover the interval [ 0 , 8 ] . This vertical slice is parallel to the axis of rotation. Now, use the shell method to calculate the volume of the solid. For each x ∈ [ 0 , 8 ] , the shell with radius x − ( − 3 ) = x + 3 and height 2 x . Now, find the volume...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 6, Problem 32CRE

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Find the volume of the solid obtained by rotating the region enclosed by the curves about the given axis.

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Chapter 6, Problem 31CRE

Chapter 6, Problem 33CRE

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Chapter 6 Solutions

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Find the volume of the solid obtained by rotating the region enclosed by the curves about the given axis.

Solution Summary: The author explains how to determine the volume of the solid obtained by rotating the region enclosed by the curves about the given axis.

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Find the volume of the solid obtained by rotating the region enclosed by the curves about the given axis.

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Chapter 6 Solutions